Intermediate Algebra for College Students

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For freshman-level, one- or two- semester courses in Developmental Algebra. The Angel Series continues to offer proven pedagogy sound exercise sets and superior student support. An emphasis on the practical applications of algebra motivates students and encourages them to see algebra as an important part of their daily lives. The student-friendly writing style uses short, clear sentences and easy-to-understand language, and the outstanding pedagogical program makes the material easy to follow and comprehend. The new editions continue to place a strong emphasis on problem solving, incorporating it as a theme throughout the texts. Angel's solid exercise sets are recognized by reviewers as of the highest standard providing a large number of problems, paired exercises, and a broad and increasing range of difficulty.

Preface

xi

To the Student

xxiv

Basic Concepts

1

(65)

Study Skills for Success in Mathematics, and Using a Calculator

2

(4)

Sets and Other Basic Concepts

6

(12)

Properties of and Operations with Real Numbers

18

(11)

Order of Operations

29

(13)

Exponents

42

(10)

Scientific Notation

52

(14)

Chapter Summary

60

(2)

Chapter Review Exercises

62

(2)

Chapter Practice Test

64

(2)

Equations and Inequalities

66

(81)

Solving Linear Equations

67

(12)

Problem Solving and Using Formulas

79

(11)

Applications of Algebra

90

(14)

Additional Application Problems

104

(11)

Solving Linear Inequalities

115

(14)

Solving Equations and Inequalities Containing Absolute Values

129

(18)

Chapter Summary

140

(1)

Chapter Review Exercises

141

(3)

Chapter Practice Test

144

(1)

Cumulative Review Test

145

(2)

Graphs and Functions

147

(89)

Graphs

148

(15)

Functions

163

(16)

Linear Functions: Graphs and Applications

179

(12)

The Slope-Intercept Form of a Linear Equation

191

(14)

The Point-Slope Form of a Linear Equation

205

(10)

The Algebra of Functions

215

(9)

Graphing Linear Inequalities

224

(12)

Chapter Summary

228

(1)

Chapter Review Exercises

229

(4)

Chapter Practice Test

233

(1)

Cumulative Review Test

234

(2)

Systems of Equations and Inequalities

236

(63)

Solving Systems of Linear Equations in Two Variables

237

(12)

Solving Systems of Linear Equations in Three Variables

249

(7)

Systems of Linear Equations: Applications and Problem Solving

256

(14)

Solving Systems of Equations Using Matrices

270

(9)

Solving Systems of Equations Using Determinants and Cramer's Rule

279

(8)

Solving Systems of Linear Inequalities

287

(12)

Chapter Summary

292

(2)

Chapter Review Exercises

294

(2)

Chapter Practice Test

296

(1)

Cumulative Review Test

297

(2)

Polynomials and Polynomial Functions

299

(86)

Addition and Subtraction of Polynomials

300

(11)

Multiplication of Polynomials

311

(10)

Division of Polynomials and Synthetic Division

321

(11)

Factoring a Monomial from a Polynomial and Factoring by Grouping

332

(8)

Factoring Trinomials

340

(11)

Special Factoring Formulas

351

(8)

A General Review of Factoring

359

(5)

Polynomial Equations

364

(21)

Chapter Summary

377

(1)

Chapter Review Exercises

378

(5)

Chapter Practice Test

383

(1)

Cumulative Review Test

384

(1)

Rational Expressions and Equations

385

(69)

The Domains of Rational Functions and Multiplication and Division of Rational Expressions

386

(10)

Addition and Subtraction of Rational Expressions

396

(12)

Complex Fractions

408

(6)

Solving Rational Equations

414

(13)

Rational Equations: Applications and Problem Solving

427

(11)

Variation

438

(16)

Chapter Summary

447

(1)

Chapter Review Exercises

448

(3)

Chapter Practice Test

451

(1)

Cumulative Review Test

452

(2)

Roots, Radicals, and Complex Numbers

454

(71)

Roots and Radicals

455

(9)

Rational Exponents

464

(9)

Simplifying Radicals

473

(8)

Adding, Subtracting, and Multiplying Radicals

481

(7)

Dividing Radicals

488

(9)

Solving Radical Equations

497

(12)

Complex Numbers

509

(16)

Chapter Summary

518

(1)

Chapter Review Exercises

519

(4)

Chapter Practice Test

523

(1)

Cumulative Review Test

524

(1)

Quadratic Functions

525

(78)

Solving Quadratic Equations by Completing the Square

526

(10)

Solving Quadratic Equations by the Quadratic Formula

536

(13)

Quadratic Equations: Applications and Problem Solving

549

(10)

Writing Equations in Quadratic Form

559

(7)

Graphing Quadratic Functions

566

(19)

Quadratic and Other Inequalities in One Variable

585

(18)

Chapter Summary

596

(1)

Chapter Review Exercises

596

(4)

Chapter Practice Test

600

(1)

Cumulative Review Test

601

(2)

Exponential and Logarithmic Functions

603

(68)

Composite and Inverse Functions

604

(12)

Exponential Functions

616

(10)

Logarithmic Functions

626

(7)

Properties of Logarithms

633

(6)

Common Logarithms

639

(7)

Exponential and Logarithmic Equations

646

(6)

Natural Exponential and Natural Logarithmic Functions

652

(19)

Chapter Summary

664

(1)

Chapter Review Exercises

665

(3)

Chapter Practice Test

668

(1)

Cumulative Review Test

669

(2)

Conic Sections

671

(41)

The Parabola and the Circle

672

(11)

The Ellipse

683

(7)

The Hyperbola

690

(8)

Nonlinear Systems of Equations and Their Applications

698

(14)

Chapter Summary

707

(1)

Chapter Review Exercises

708

(2)

Chapter Practice Test

710

(1)

Cumulative Review Test

710

(2)

Sequences, Series, and the Binomial Theorem

712

(39)

Sequences and Series

713

(8)

Arithmetic Sequences and Series

721

(7)

Geometric Sequences and Series

728

(12)

The Binomial Theorem

740

(11)

Chapter Summary

745

(1)

Chapter Review Exercises

746

(3)

Chapter Practice Test

749

(1)

Cumulative Review Test

749

(2)

Appendix Geometric Formulas

751

Answers

1

(1)

Index

1

(1)

Photo Credits

1

This book was written for college students who have successfully completed a first course in elementary algebra. My primary goal was to write a book that students can read, understand, and enjoy. To achieve this goal I have used short sentences, clear explanations, and many detailed, worked-out examples. I have tried to make the book relevant to college students by using practical applications of algebra throughout the text. Features of the Text Full-Color Format.Color is used pedagogically in the following ways: Important definitions and procedures are color screened. Color screening or color type is used to make other important items stand out. Artwork is enhanced and clarified with use of multiple colors. The full-color format allows for easy identification of important features by students. The full-color format makes the text more appealing and interesting to students. Readability.One of the most important features of the text is its readability. The book is very readable, even for those with weak reading skills. Short, clear sentences are used and more easily recognized, and easy-to-understand language is used whenever possible. Accuracy.Accuracy in a mathematics text is essential. To ensure accuracy in this book, mathematicians from around the country have read the pages carefully for typographical errors and have checked all the answers. Connections.Many of our students do not thoroughly grasp new concepts the first time they are presented. In this text, we encourage students to make connections. That is, we introduce a concept, then later in the text briefly reintroduce it and build upon it. Often an important concept is used in many sections of the text. Students are reminded where the material was seen before, or where it will be used again. This also serves to emphasize the importance of the concept. Important concepts are also reinforced throughout the text in the Cumulative Review Exercises and Cumulative Review Tests. Chapter Opening Application.Each chapter begins with a real-life application related to the material covered in the chapter. By the time students complete the chapter, they should have the knowledge to work the problem. A Look Ahead.This feature at the beginning of each chapter gives students a preview of the chapter. This feature also indicates where this material will be used again in other chapters of the book. This material helps students see the connections between various topics in the book and the connection to real-world situations. The Use of Icons.At the beginning of each chapter and of each section, a variety of icons are illustrated. These icons are provided to tell students where they may be able to get extra help if needed. There are icons for theStudent's Solution Manual;theStudent's Study Guide;CDs and videotapes; Math Pro 4/5 Software;thePrentice Hall Tutor Center;and theAngel Website.Each of these items will be discussed shortly. Keyed Section Objectives.Each section opens with a list of skills that the student should learn in that section. The objectives are then keyed to the appropriate portions of the sections with red numbers such as 1. Problem Solving.George Polya's five-step problem-solving procedure is discussed in Section 1.2. Throughout the book problem solving and Polya's problem-solving procedure are emphasized. Practical Applications.Practical applications of algebra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. The problem-solving approach used throughout this text gives students ample practice in setting up and solving application problems. The use of practical applications motivates students. Detailed; Worked-Out Examples.A wealth of examples have been worked o